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Open Computer Science

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A note on the multiplication of sparse matrices

Keivan Borna
  • Faculty of Mathematics and Computer Science, Kharazmi University, Tehran, Iran
  • School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. 19395-5746, Tehran, Iran
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/ Sohrab Fard
Published Online: 2014-03-12 | DOI: https://doi.org/10.2478/s13537-014-0201-x


We present a practical algorithm for multiplication of two sparse matrices. In fact if A and B are two matrices of size n with m 1 and m 2 non-zero elements respectively, then our algorithm performs O(min{m 1 n, m 2 n, m 1 m 2}) multiplications and O(k) additions where k is the number of non-zero elements in the tiny matrices that are obtained by the columns times rows matrix multiplication method. Note that in the useful case, k ≤ m 2 n. However, in Proposition 3.3 and Proposition 3.4 we obtain tight upper bounds for the complexity of additions. We also study the complexity of multiplication in a practical case where non-zero elements of A (resp. B) are distributed independently with uniform distribution among columns (resp. rows) of them and show that the expected number of multiplications is O(m 1 m 2/n). Finally a comparison of number of required multiplications in the naïve matrix multiplication, Strassen’s method and our algorithm is given.

Keywords: algorithms; matrix multiplication; sparse matrices; tiny matrices

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About the article

Published Online: 2014-03-12

Published in Print: 2014-03-01

Citation Information: Open Computer Science, Volume 4, Issue 1, Pages 1–11, ISSN (Online) 2299-1093, DOI: https://doi.org/10.2478/s13537-014-0201-x.

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© 2014 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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